DSAT DSAT Geometry and Trigonometry

Question 1

A circle has a radius of 7. What is the area of the circle?

Accepted Answer

49π

Answer

The area of a circle is πr², so with r = 7, the area is π(7²) = 49π.

Question 2

In a right triangle, the two legs measure 9 and 12. What is the length of the hypotenuse?

Accepted Answer

15

Answer

Using the Pythagorean theorem: 9² + 12² = 81 + 144 = 225, and √225 = 15.

Question 3

What is the volume of a rectangular prism with length 5, width 4, and height 3?

Accepted Answer

60

Answer

Volume of a rectangular prism = length × width × height = 5 × 4 × 3 = 60.

Question 4

Two parallel lines are cut by a transversal. If one interior angle measures 65°, what is the measure of the co-interior (same-side interior) angle?

Accepted Answer

115°

Answer

Co-interior angles (same-side interior) are supplementary, so they add up to 180°; 180° − 65° = 115°.

Question 5

A triangle has angles measuring 45°, 90°, and 45°. If the hypotenuse is 10, what is the length of each leg?

Accepted Answer

5√2

Answer

In a 45-45-90 triangle, each leg = hypotenuse ÷ √2 = 10 ÷ √2 = 5√2.

(DSAT) Digital SAT Practice Test